All items can be found via searching various locations on the world map, or trading with passing traders.
The game uses an item quality system ranging from 1★ to 3★, higher quality items always have a higher trade value and are required by some higher tier constructions. Equiptment and weapons of higher quality will last longer before breaking down and needing repairs.
Items of higher quality can be used for crafting that demands lower levels of quality, but not vice-versa. Example: 3 star nails can be used for crafting that only requires 1 star nails, but not the other way around.
The goals that increase the chance for Excellent quality seems to be the best method to increase quality right now, making most items your survivors craft rated 3 stars once you have crafted 100 items in total. This applies to crafted and cooked items, first and foremost.
For higher quality raw materials, scavenging, foraging, combat and hunting are the main methods to procure them at the moment. Work Sites always produce 3★ items.